Speaking on NBC’s “Meet the Press,” Mr. Kaine said there have been no specific discussions about a replacement for the massive proposal, but he said they’ll “never close the door” on any large-scale trade deals, signaling that TPP by a different name could be on the horizon if Democrats defeat Republican Donald Trump.

“Hillary and I haven’t talked about that question directly. … But look, we aren’t against trade. We want to find export markets for American businesses, because they’ll be able to add workers the more they export,” the Virginia Democrat said. “If we can find deals that meet those goals — more jobs, higher wages and good for national security and good enforcement provisions — we’re open to them. So, no, you never close the door if you can get a deal that’s good for American workers and our economy.”

The comments again open Mrs. Clinton to charges of hypocrisy on TPP, an Obama administration-backed U.S. trade deal with 12 Pacific nations. The plan also enjoys support from top Republicans in Congress, though not GOP presidential nominee Donald Trump.

Mrs. Clinton famously called the TPP the “gold standard” of trade deals while she served as secretary of state. But during a long, bitter primary battle with Sen. Bernard Sanders, who vehemently opposed the deal, Mrs. Clinton switched her position.

She said the agreement in its final form simply didn’t meet her high standards, though popular political wisdom has been that Mrs. Clinton changed her stance in order to appeal to progressive Democrats in the party primary.

Newly released Clinton campaign emails show the former first lady and her top aides grappling over Mrs. Clinton’s clear flip-flop on the issue and how it would play politically.

“I think opposing that would be a huge flip-flop. She can say that as president she would work to change it. She can say that it can be better. But I think she should support it,” Clinton adviser Ron Klain wrote in an October 2015 message, just before Mrs. Clinton announced her opposition.

“TPP would be lethal with labor,” campaign manager Robby Mook responded, saying that top unions such as AFSCME and SEIU may not endorse the former first lady if she backed TPP. They did endorse Mrs. Clinton just weeks after she announced her opposition to TPP and despite a challenge from Mr. Sanders, who had a much longer history of opposing free trade deals.

Mr. Kaine too had been supportive of the deal but announced his opposition after being named to the Democratic ticket. On Sunday he flatly said that the Clinton campaign did not ask him to change positions on TPP before he became the vice presidential nominee.

Meanwhile, Mr. Trump has used Mrs. Clinton’s switch on TPP as a populist political weapon in the general election, and has told voters the former secretary will reverse course and back the agreement if she becomes president.

“She wants it,” Mr. Trump said during last Wednesday’s presidential debate. “She lied when she said she didn’t call it the gold standard … she totally lied. She did call it the gold standard.”

Mrs. Clinton did use the phrase “gold standard” in describing the deal, but has said she changed her mind after seeing the final pact.

“It didn’t meet my test,” she said at the debate. “I’ve had the same test. Does it create jobs, raise incomes and further our national security? I’m against it now. I’ll be against it after the election. I’ll be against it when I’m president.”

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